A velocity/stress mixed stabilized nodal finite element for elastodynamics: analysis and computations with strongly and weakly enforced boundary conditions
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Publication:2310032
DOI10.1016/j.cma.2017.07.018zbMath1439.74148OpenAlexW2737558995MaRDI QIDQ2310032
Publication date: 6 April 2020
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2017.07.018
wave equationelastodynamicsweak boundary conditionsstabilized methodsvariational multiscale analysisnodal stress or nodal strain
Finite element methods applied to problems in solid mechanics (74S05) Linear waves in solid mechanics (74J05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) PDEs in connection with mechanics of deformable solids (35Q74)
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Cites Work
- Stabilized finite element method for viscoplastic flow: formulation with state variable evolution
- Remarks on the stability of enhanced strain elements in finite elasticity and elastoplasticity
- A continuous space-time finite element method for the wave equation
- A Priori Estimates for Mixed Finite Element Approximations of Second-Order Hyperbolic Equations with Absorbing Boundary Conditions
- A class of mixed assumed strain methods and the method of incompatible modes
- Mixed Methods for Elastodynamics with Weak Symmetry
- Galilean invariance and stabilized methods for compressible flows
- An adaptive stabilization strategy for enhanced strain methods in non‐linear elasticity
- F‐bar‐based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking
- On the enhancement of low-order mixed finite element methods for the large deformation analysis of diffusion in solids
- Stabilized finite element method for viscoplastic flow: Formulation and a simple progressive solution strategy
- Simple stabilizing matrices for the computation of compressible flows in primitive variables
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A computational framework for polyconvex large strain elasticity for geometrically exact beam theory
- A vertex centred finite volume Jameson-Schmidt-Turkel (JST) algorithm for a mixed conservation formulation in solid dynamics
- A conservative nodal variational multiscale method for Lagrangian shock hydrodynamics
- Mixed stabilized finite element methods in nonlinear solid mechanics. I: Formulation
- Mixed stabilized finite element methods in nonlinear solid mechanics. II: Strain localization
- Weak boundary conditions for wave propagation problems in confined domains: formulation and implementation using a variational multiscale method
- Development of a stabilised Petrov-Galerkin formulation for conservation laws in Lagrangian fast solid dynamics
- A priori estimates for mixed finite element methods for the wave equation
- A new finite element formulation for computational fluid dynamics. VIII. The Galerkin/least-squares method for advective-diffusive equations
- Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity: motivation, formulation, and numerical examples
- On finite element formulations for nearly incompressible linear elasticity
- A new finite element formulation for computational fluid dynamics. I: Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics
- A new finite element formulation for computational fluid dynamics. IV: A discontinuity-capturing operator for multidimensional advective-diffusive systems
- A new finite element formulation for computational fluid dynamics. II. Beyond SUPG
- A new finite element formulation for computational fluid dynamics. III: The generalized streamline operator for multidimensional advective- diffusive systems
- A new finite element formulation for computational fluid dynamics. V: Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations
- Two classes of mixed finite element methods
- A family of mixed finite elements for the elasticity problem
- A new finite element formulation for computational fluid dynamics. VI. Convergence analysis of the generalized SUPG formulation for linear time- dependent multidimensional advective-diffusive systems
- A new finite element formulation for computational fluid dynamics. VII. The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces
- A new family of stable elements for nearly incompressible elasticity based on a mixed Petrov-Galerkin finite element formulation
- Numerical algorithms for strong discontinuities in elastic-plastic solids
- A new finite element formulation for computational fluid dynamics. IX: Fourier analysis of space-time Galerkin/least-squares algorithms
- Mixed finite element methods - reduced and selective integration techniques: a unification of concepts
- Discontinuous Galerkin finite element methods for second order hyperbolic problems
- A second-order Godunov algorithm for two-dimensional solid mechanics
- Higher order stabilized finite element method for hyperelastic finite deformation
- Design of simple low order finite elements for large strain analysis of nearly incompressible solids
- An iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics.
- Mixed linear/linear simplicial elements for incompressible elasticity and plasticity.
- A new stabilized enhanced strain element with equal order of interpolation for soil consolidation problems.
- A stabilised Petrov-Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics
- A first order hyperbolic framework for large strain computational solid dynamics. I: Total Lagrangian isothermal elasticity
- A computational framework for polyconvex large strain elasticity
- A mixed three-field FE formulation for stress accurate analysis including the incompressible limit
- A hybridizable discontinuous Galerkin formulation for non-linear elasticity
- Mixed stabilized finite element methods in nonlinear solid mechanics. III: compressible and incompressible plasticity
- On mixed finite element methods for linear elastodynamics
- Space-time finite element methods for elastodynamics: Formulations and error estimates
- A stabilized formulation for incompressible plasticity using linear triangles and tetrahedra
- On numerically accurate finite element solutions in the fully plastic range
- Mixed finite elements for elasticity
- A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations.
- Theory and practice of finite elements.
- A unified approach to compressible and incompressible flows
- A comparative study of different sets of variables for solving compressible and incompressible flows
- A stabilized mixed finite element method for finite elasticity. Formulation for linear displacement and pressure interpolation
- Explicit mixed strain-displacement finite element for dynamic geometrically non-linear solid mechanics
- Implicit finite incompressible elastodynamics with linear finite elements: a stabilized method in rate form
- The double absorbing boundary method for a class of anisotropic elastic media
- Numerical solution of the acoustic wave equation using Raviart-Thomas elements
- An upwind vertex centred finite volume solver for Lagrangian solid dynamics
- A first order hyperbolic framework for large strain computational solid dynamics. II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity
- A new framework for large strain electromechanics based on convex multi-variable strain energies: variational formulation and material characterisation
- A new framework for large strain electromechanics based on convex multi-variable strain energies: finite element discretisation and computational implementation
- A framework for residual-based stabilization of incompressible finite elasticity: stabilized formulations and \(\overline F\) methods for linear triangles and tetrahedra
- Stabilized shock hydrodynamics. I: A Lagrangian method
- Stabilized shock hydrodynamics. II: Design and physical interpretation of the SUPG operator for Lagrangian computations
- A discourse on Galilean invariance, SUPG stabilization, and the variational multiscale framework
- An analysis of some mixed-enhanced finite element for plane linear elasticity
- Error-bounds for finite element method
- Approximation des problèmes aux limites non homogènes pour des opérateurs non linéaires
- Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
- Stabilized finite element formulation for elastic--plastic finite deformations
- A Nitsche method for wave propagation problems in time domain
- Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity: analytical estimates
- Stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications
- Polygonal finite elements for finite elasticity
- A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach
- A 10-node composite tetrahedral finite element for solid mechanics
- STRESS–VELOCITY COMPLETE RADIATION BOUNDARY CONDITIONS
- NONCONFORMING MIXED ELEMENTS FOR ELASTICITY
- A generalized view on Galilean invariance in stabilized compressible flow computations
- A higher-order Godunov method for modeling finite deformation in elastic-plastic solids
- The Riemann Problem for Longitudinal Motion in an Elastic-Plastic Bar
- CBS-based stabilization in explicit solid dynamics
- A stabilized nodally integrated tetrahedral
- Discontinuous Galerkin methods for non-linear elasticity
- A Stabilized Mixed Finite Element Method for Nearly Incompressible Elasticity
- A uniform nodal strain tetrahedron with isochoric stabilization
- Mixed finite element methods for linear elasticity with weakly imposed symmetry
- Generalization of selective integration procedures to anisotropic and nonlinear media
- Dynamic Fracture Mechanics
- Mixed and Hybrid Finite Element Methods
- On stability and convergence of projection methods based on pressure Poisson equation
- Triangles and tetrahedra in explicit dynamic codes for solids
- Tetrahedral composite finite elements
- A mixed displacement-pressure formulation for numerical analysis of plastic failure
- Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes
- F‐bar aided edge‐based smoothed finite element method using tetrahedral elements for finite deformation analysisof nearly incompressible solids
- Finite calculus formulation for incompressible solids using linear triangles and tetrahedra
- An assessment of the average nodal volume formulation for the analysis of nearly incompressible solids under finite strains
- A Priori Error Estimates for Mixed Finite Element Approximations of the Acoustic Wave Equation
